Oh NOW I understand lol. Yeah the width of the secondary hull is wide like a tree trunk. The idea behind that is a frontal silhouette that looks similar to the excelsior.
From an interior design standpoint, the entire saucer is designated for habitation only (complete with large hydroponics park), with all science labs, equipment and cargo bays in the thick trunk of the secondary hull. Kind of like the highrise living quarters of the ship sitting on top of the street level business district. If that makes ANY sense at all.
As far as captain's yachts are concerned, the saucer's shuttle bay holds two axillary craft similar in size to the Cousteau. Smaller runabouts and shuttle craft are in the aft bay. So there aren't any craft that detach from the exterior of the ship.